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3.
Results and Discussion
In this section, axial deformation behaviors of straight and truncated (with angles of 1,5° and 3°) tube-like
structures under dynamic loading conditions were investigated.For truncated and straight circular cross-
section members, rigid wall force-displacement graph is given in Figure 3, the mean force-displacement and
absorbed energy displacement graphs are given in Figure 4. The deformation patterns of straight and truncated
(with angle of 1,5°) members with wall thicknesses of 4 and 6 mm are given in Figure 5.
It is seen from Figure 7 that the local maximum and minimum force values are comprised during the
formation of the folds in the axial deformation of the energy absorbing members. In the formation of the first
fold the rigid wall force value reaches its maximum and then decreases suddenly. During the formation of the
second and subsequent folds, the force fluctuates between the local maximum and minimum values.
Ramazan Özmen
et al.
PENVol. 5, No. 3, November 2017, pp. 387
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Figure 3. Deformation states of straight and truncated cone members versus time
Al Galib and Limam[17] emphasized this situation that, the initial force required to form the first fold of the
member should be high because there is no deformation at the beginning of the tube. When the formation of
the first fold, deformations occur in the member and that these deformations reduce the subsequent peak
forces.
If the member has the capability to absorb the current impact energy, the force value reaches zero at the rigid
wall force-displacement graph. Otherwise, the member loses its energy absorbing ability and starts to behave
like a rigid body.When the rigid plate wall force-displacement graph is examined (Fig. 3), it is seen that the
rigid wall force increases again towards the end of the analysis due to the loss of energy absorbing ability of
members with 4 mm thickness.
Figure 4. Rigid wall force-displacement fortruncatedand circular cross-section members
Ramazan Özmen
et al.
PENVol. 5, No. 3, November 2017, pp. 387
–
395
391
Figure 5. Mean force and absorbed energy versus displacement for 1.5° tapered and straight members
According to the average deformation force-rigid plate displacement graph (Fig. 4), it is seen that the average
deformation force is increases as the thickness increases because a rigid structure is obtained at the same
member weight. Though the weight is the same, the member becomes more rigid as the thickness increases.
In this study, axial deformation behaviors of equally weighted members were examined, hence the cross-
sectional dimensions change with increasing thickness. Even though the thickness and the cross-sectional
properties of the members change, the amount of material required for plastic deformation remains the same.
In this case, the increase of the average deformation force is due to the increase of the full plastic bending
moment
= 𝜎 ℎ /4
required for buckling when the thickness increases. Figure 4 shows a comparison
between straight and truncated members, it is seen that the average deformation force values of straight
members are higher than those with truncated members with the same wall thicknesses.
The amount of maximum deformation and the change in initial peak force with respect to thickness and taper
angle for the members in the form of straight and truncated cone are given in Figure 6.
Figure 6. The effect of taper angle on maximum deformation of the member and initial peak force
As can be seen from the Figure 6, the amount of maximum deformation decreases as the thickness of the
member increases. When the effect of the taper angle on the maximum deformation is examined for the same
thickness elements, the amount of maximum deformation increases as the taper angle of the member
increases.
The low initial peak force is desirable feature for energy absorbing members. Therefore, when the change of
the first peak force with the taper angle is examined, it is seen that as the taper angle increases, the initial peak
force decreases. The reduction in the initial peak force is very small for the straight elements, but this
reduction is more pronounced for the truncated elements. The cross-sectional area of the member is decreased
to provide the same weight as the thickness of the element increased. From the initial peak force vs angle
graph, the initial peak force decreases even if the thickness of the member increases.
Ramazan Özmen
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